data structures and data types - lecture 2pitt.edu/~njc23/lecture2.pdf · data structures and data...

Data Structures and Data Types

Lecture 2

Nicholas Christian

BIOST 2094 Spring 2011

Vectors Matrices Arrays Lists Dataframes Numeric Logical Character Factor Dates Missing Data

Outline

1. Data Structures

� Vectors� Matrices� Arrays� Lists� Dataframes

2. Data Types

� Numeric� Logical� Character� Factor� Dates� Missing Data

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Vectors

� A vector is an ordered collection of objects of the same type� The function c(...) concatenates its arguments to form a vector� To create a patterned vector

� : Sequence of integers� seq() General sequence� rep() Vector of replicated elements

> v1 <- c(2.5, 4, 7.3, 0.1)

> v1

[1] 2.5 4.0 7.3 0.1

> v2 <- c("A", "B", "C", "D")

> v2

[1] "A" "B" "C" "D"

> v3 <- -3:3

> v3

[1] -3 -2 -1 0 1 2 3

> seq(0, 2, by=0.5)

[1] 0.0 0.5 1.0 1.5 2.0

> seq(0, 2, len=6)

[1] 0.0 0.4 0.8 1.2 1.6 2.0

> rep(1:5, each=2)

[1] 1 1 2 2 3 3 4 4 5 5

> rep(1:5, times=2)

[1] 1 2 3 4 5 1 2 3 4 5

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Reference Elements of a Vector

� Use [ ] with a vector/scalar of positions to reference elements of a vector� Include a minus sign before the vector/scalar to remove elements

> x <- c(4, 7, 2, 10, 1, 0)

> x[4]

[1] 10

> x[1:3]

[1] 4 7 2

> x[c(2,5,6)]

[1] 7 1 0

> x[-3]

[1] 4 7 10 1 0

> x[-c(4,5)]

[1] 4 7 2 0

> x[x>4]

[1] 7 10

> x[3] <- 99

> x

[1] 4 7 99 10 1 04 of 45


which() and match()

� Additional functions that will return the indices of a vector

� which() Indices of a logical vector where the condition is TRUE

� which.max() Location of the (first) maximum element of a numeric vector� which.min() Location of the (first) minimum element of a numeric vector� match() First position of an element in a vector

> x <- c(4, 7, 2, 10, 1, 0)

> x>=4

[1] TRUE TRUE FALSE TRUE FALSE FALSE

> which(x>=4)

[1] 1 2 4

> which.max(x)

[1] 4

> x[which.max(x)]

[1] 10

> max(x)

[1] 10

> y <- rep(1:5, times=5:1)

> y

[1] 1 1 1 1 1 2 2 2 2 3 3 3 4 4 5

> match(1:5, y)

[1] 1 6 10 13 15

> match(unique(y), y)

[1] 1 6 10 13 15

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Vector Operations

� When vectors are used in math expressions the operations are performedelement by element

> x <- c(4,7,2,10,1,0)

> y <- x^2 + 1

> y

[1] 17 50 5 101 2 1

> x*y

[1] 68 350 10 1010 2 0

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Useful Vector Functionssum(x) prod(x) Sum/product of the elements of x

cumsum(x) cumprod(x) Cumulative sum/product of the elements of x

min(x) max(x) Minimum/Maximum element of x

mean(x) median(x) Mean/median of x

var(x) sd(x) Variance/standard deviation of x

cov(x,y) cor(x,y) Covariance/correlation of x and y

range(x) Range of x

quantile(x) Quantiles of x for the given probabilitiesfivenum(x) Five number summary of x

length(x) Number of elements in x

unique(x) Unique elements of x

rev(x) Reverse the elements of x

sort(x) Sort the elements of x

which() Indices of TRUEs in a logical vectorwhich.max(x) which.min(x) Index of the max/min element of x

match() First position of an element in a vector

union(x, y) Union of x and y

intersect(x, y) Intersection of x and y

setdiff(x, y) Elements of x that are not in y

setequal(x, y) Do x and y contain the same elements?7 of 45


Matrices

� A matrix is just a two-dimensional generalization of a vector� To create a matrix,

matrix(data=NA, nrow=1, ncol=1, byrow = FALSE, dimnames = NULL)

data a vector that gives data to fill the matrix; if data does not have enoughelements to fill the matrix, then the elements are recycled.

nrow desired number of rowsncol desired number of columnsbyrow if FALSE (default) matrix is filled by columns, otherwise by rows

dimnames (optional) list of length 2 giving the row and column names respectively, listnames will be used as names for the dimensions

> x <- matrix(c(5,0,6,1,3,5,9,5,7,1,5,3), nrow=3, ncol=4, byrow=TRUE,

+ dimnames=list(rows=c("r.1", "r.2", "r.3"),

+ cols=c("c.1", "c.2", "c.3", "c.4")))

> x

cols

rows c.1 c.2 c.3 c.4

r.1 5 0 6 1

r.2 3 5 9 5

r.3 7 1 5 38 of 45


Reference Elements of a Matrix

� Reference matrix elements using the [ ] just like with vectors, but now with2-dimensions

> x <- matrix(c(5,0,6,1,3,5,9,5,7,1,5,3), nrow=3, ncol=4, byrow=TRUE)

> x

[,1] [,2] [,3] [,4]

[1,] 5 0 6 1

[2,] 3 5 9 5

[3,] 7 1 5 3

> x[2,3] # Row 2, Column 3

[1] 9

> x[1,] # Row 1

[1] 5 0 6 1

> x[,2] # Column 2

[1] 0 5 1

> x[c(1,3),] # Rows 1 and 3, all Columns

[,1] [,2] [,3] [,4]

[1,] 5 0 6 1

[2,] 7 1 5 3

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� We can also reference parts of a matrix by using the row or column names

� Sometimes it is better to reference a row/column by its name rather thanby the numeric index. For example, if a program adds or permutes thecolumns of a matrix then the numeric index of the columns may change. Asa result you might reference the wrong column of the new matrix if you usethe old index number. However the name of each column will not change.

� Reference matrix elements using the [ ] but now use the column or rowname, with quotations, inplace of the index number

� You don’t have to specify the names when you create a matrix. To get orset the column, row, or both dimension names of A:

colnames(A)

rownames(A)

dimnames(A)

� Can also name the elements of a vector, c("name.1"=1, "name.2"=2).Use the function names() to get or set the names of vector elements.

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> N <- matrix(c(5,8,3,0,4,1), nrow=2, ncol=3, byrow=TRUE)

> colnames(N) <- c("c.1", "c.2", "c.3")

> N

c.1 c.2 c.3

[1,] 5 8 3

[2,] 0 4 1

> N[,"c.2"] # Column named "c.2"

[1] 8 4

> colnames(N)

[1] "c.1" "c.2" "c.3"

> M <- diag(2)

> (MN <- cbind(M, N)) # Placing the expression in parentheses

c.1 c.2 c.3 # will print the result

[1,] 1 0 5 8 3

[2,] 0 1 0 4 1

> MN[,2] # Column 2

[1] 0 1

> MN[,"c.2"] # Column named "c.2"

[1] 8 4

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Matrix Operations

� When matrices are used in math expressions the operations are performedelement by element.

� For matrix multiplication use the %*% operator

� If a vector is used in matrix multiplication, it will be coerced to either a rowor column matrix to make the arguments conformable. Using %*% on twovectors will return the inner product (%o% for outer product) as a matrixand not a scalar. Use either c() or as.vector() to convert to a scalar.

> A <- matrix(1:4, nrow=2)

> B <- matrix(1, nrow=2, ncol=2)

> A*B

[,1] [,2]

[1,] 1 3

[2,] 2 4

> A%*%B

[,1] [,2]

[1,] 4 4

[2,] 6 6

> y <- 1:3

> y%*%y

[,1]

[1,] 14

> A/(y%*%y)

Error in A/(y%*%y):non-conformable arrays

> A/c(y%*%y)

[,1] [,2]

[1,] 0.07142857 0.2142857

[2,] 0.14285714 0.2857143

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Useful Matrix Functionst(A) Transpose of A

det(A) Determinate of A

solve(A, b) Solves the equation Ax=b for xsolve(A) Matrix inverse of A

MASS::ginv(A) Generalized inverse of A (MASS package)eigen(A) Eigenvalues and eigenvectors of A

chol(A) Choleski factorization of A

diag(n) Create a n×n identity matrixdiag(A) Returns the diagonal elements of a matrix A

diag(x) Create a diagonal matrix from a vector xlower.tri(A),upper.tri(A) Matrix of logicals indicating lower/upper

triangular matrix

apply() Apply a function to the margins of a matrixrbind(...) Combines arguments by rowscbind(...) Combines arguments by columns anddim(A) Dimensions of A

nrow(A), ncol(A) Number of rows/columns of A

colnames(A), rownames(A) Get or set the column/row names of A

dimnames(A) Get or set the dimension names of A

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apply()

� The apply() function is used for applying functions to the margins of amatrix, array, or dataframes.

apply(X, MARGIN, FUN, ...)

X A matrix, array or dataframeMARGIN Vector of subscripts indicating which margins to apply the function to

1=rows, 2=columns, c(1,2)=rows and columnsFUN Function to be applied... Optional arguments for FUN

� You can also use your own function (more on this later)

> (x <- matrix(1:12, nrow=3, ncol=4))

[,1] [,2] [,3] [,4]

[1,] 1 4 7 10

[2,] 2 5 8 11

[3,] 3 6 9 12

> apply(x, 1, sum) # Row totals

[1] 22 26 30

> apply(x, 2, mean) # Column means

[1] 2 5 8 11

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Example - Simulating Survival Data

� The apply() function is great for simulating survival data. Suppose wewant to simulate n = 10 observations where, the event times T follow anexponential distribution with mean λ = 0.25 and the censoring times C aredistributed uniformly from 0 to 1. Then the observed data is,X = min(T ,C ) and δ = I (T < C ).

# Sample size

n = 10

# Generate event and censor times (look at the documentation to see

# how R parameterizes the exponential distribution)

event <- rexp(n, 4)

censor <- runif(n)

# Select the minimum time and create an indicator variable

time <- apply(cbind(censor, event), 1, min)

index <- apply(cbind(censor, event), 1, which.min)-1

cbind(event, censor, time, index) # Verify

data <- cbind(time, index) # Simulated dataset15 of 45


Arrays

� An array is a multi-dimensional generalization of a vector

� To create an array,

array(data = NA, dim = length(data), dimnames = NULL)

data A vector that gives data to fill the array; if data does not have enoughelements to fill the matrix, then the elements are recycled.

dim Dimension of the array, a vector of length one or more giving the maximumindices in each dimension

dimnames Name of the dimensions, list with one component for each dimension, eitherNULL or a character vector of the length given by dim for that dimension.The list can be named, and the list names will be used as names for thedimensions.

� Values are entered by columns

� Like with vectors and matrices, when arrays are used in math expressionsthe operations are performed element by element.

� Also like vectors and matrices, the elements of an array must all be of thesame type (numeric, character, logical, etc.)

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Arrays

� Sample 2 × 3 × 2 array,

> w <- array(1:12, dim=c(2,3,2),

dimnames=list(c("A","B"), c("X","Y","Z"), c("N","M")))

> w

, , N

X Y Z

A 1 3 5

B 2 4 6

, , M

X Y Z

A 7 9 11

B 8 10 12

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Reference Elements of an Array

� Reference array elements using the [ ] just like with vectors and matrices,but now with more dimensions

> w <- array(1:12, dim=c(2,3,2),

dimnames=list(c("A","B"), c("X","Y","Z"), c("N","M")))

> w[2,3,1] # Row 2, Column 3, Matrix 1

[1] 6

> w[,"Y",] # Column named "Y"

N M

A 3 9

B 4 10

> w[1,,] # Row 1

N M

X 1 7

Y 3 9

Z 5 11

> w[1:2,,"M"] # Rows 1 and 2, Matrix "M"

X Y Z

A 7 9 11

B 8 10 1218 of 45


Useful Array Functions

apply() Apply a function to the margins of an arrayaperm() Transpose an array by permuting its dimensionsdim(x) Dimensions of x

dimnames(x) Get or set the dimension names of x

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apply()

� We can use the apply() function for more then one dimension

� For a 3-dimensional array there are now three margins to apply the functionto: 1=rows, 2=columns, and 3=matrices.

# Column sums

> apply(w, 2, sum)

X Y Z

18 26 34

# Row and matrix sums

> apply(w, c(1,3), sum)

N M

A 9 27

B 12 30

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Lists

� A list is a general form of a vector, where the elements don’t need to be ofthe same type or dimension.

� The function list(...) creates a list of the arguments� Arguments have the form name=value. Arguments can be specified with

and without names.

> x <- list(num=c(1,2,3), "Nick", identity=diag(2))

> x

$num

[1] 1 2 3

[[2]]

[1] "Nick"

$identity

[,1] [,2]

[1,] 1 0

[2,] 0 1

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Reference Elements of a List

� Elements of a list can be referenced using [ ] as well as [[ ]] or $.

> x <- list(num=c(1,2,3), "Nick", identity=diag(2))

> x[[2]] # Second element of x

[1] "Nick"

> x[["num"]] # Element named "num"

[1] 1 2 3

> x$identity # Element named "identity"

[,1] [,2]

[1,] 1 0

[2,] 0 1

> x[[3]][1,] # First row of the third element

[1] 1 0

> x[1:2] # Create a sublist of the first two elements

$num

[1] 1 2 3

[[2]]

[1] "Nick"22 of 45


Useful List Functions

lapply() Apply a function to each element of a list, returns a listsapply() Same as lapply(), but returns a vector or matrix by defaultvapply() Similiar to sapply(), but has a pre-specified type of return valuereplicate() Repeated evaluation of an expression, useful for replicating lists

unlist(x) Produce a vector of all the components that occur in x

length(x) Number of objects in x

names(x) Names of the objects in x

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Example - lapply(), sapply(), vapply()

� First generate a list L of seven different vectors. Then calculate the fivenumber summary of each vector in L using lapply(), sapply() andvapply().

# List of seven different vectors

L <- lapply(3:9, seq)

# Calculate the five number summary for each vector in L

lapply(L, fivenum)

sapply(L, fivenum)

vapply(L, fivenum, c(Min.=0, "1st Quart"=0, Median=0, "3rd Qu"=0, Max.=0))

� Since 3:9 is not a list, R calls as.list(3:9) which coerces the vector 3:9to a list of length 7 where each number is an element of L. Also note thatseq(n) is the same as 1:n.

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Dataframes

� R refers to datasets as dataframes� A dataframe is a matrix-like structure, where the columns can be of

different types. You can also think of a dataframe as a list. Each column isan element of the list and each element has the same length.

� A dataframe is the fundamental data structure used by R ’s statisticalmodeling functions

� Lecture 8 will be completely devoted to the managment and use ofdataframes

Population Income Illiteracy Life.Exp state.region

Alabama 3615 3624 2.1 69.05 South

Alaska 365 6315 1.5 69.31 West

Arizona 2212 4530 1.8 70.55 West

Arkansas 2110 3378 1.9 70.66 South

California 21198 5114 1.1 71.71 West

Colorado 2541 4884 0.7 72.06 West

Connecticut 3100 5348 1.1 72.48 Northeast

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Numeric

� Technically, numeric data in R can be either double or integer, but inpractice numeric data is almost always double (type double refers to realnumbers). See ?integer and ?double.

� .Machine outputs numeric characteristics of the machine running R, suchas the largest integer or the machine’s precision

� format() formats an object for pretty printing. format() is a genericfunction that is used with other types of objects. See ?format() foradditional arguments.

> # trim - If FALSE right justified with common width

> format(c(1,10,100,1000), trim = FALSE)

[1] " 1" " 10" " 100" "1000"

> format(c(1,10,100,1000), trim = TRUE)

[1] "1" "10" "100" "1000"

> # nsmall - Minimum number of digits to the right of the decimal point

> format(13.7, nsmall = 3)

[1] "13.700"

> # scientific - Use scientific notation

> format(2^16, scientific = TRUE)

[1] "6.5536e+04"26 of 45


Logical� Logical values are represented by the reserved words TRUE and FALSE in all

caps or simply T and F.!x NOT x

x & y x AND y elementwise, returns a vectorx && y x AND y, returns a single valuex | y x OR y elementwise, returns a vectorx || y x OR y, returns a single valuexor(x,y) Exclusive OR of x and y, elementwisex %in% y x IN y

x < y x < y

x > y x > y

x <= y x ≤ y

x >= y x ≥ y

x == y x = y

x ! = y x 6= y

isTRUE(x) TRUE if x is TRUE

all(...) TRUE if all arguments are TRUE

any(...) TRUE if at least one argument is TRUE

identical(x,y) Safe and reliable way to test two objects for being exactly equalall.equal(x,y) Test if two objects are nearly equal

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Example - Logical Operations

> x <- 1:10

> (x%%2==0) | (x > 5) # What elements of x are even or greater than 5?

[1] FALSE TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE

> x[(x%%2==0) | (x > 5)]

[1] 2 4 6 7 8 9 10

> y <- 5:15 # What elements of x are in y?

> x %in% y

[1] FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE

> x[x %in% y]

[1] 5 6 7 8 9 10

> any(x>5) # Are any elements of x greater then 5?

[1] TRUE

> all(x>5) # Are all the elements of x greater then 5?

[1] FALSE

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Isn’t that equal?

� In general, logical operators may not produce a single value and may returnan NA if an element is NA or NaN.

� If you must get a single TRUE or FALSE, such as with if expressions, youshould NOT use == or !=. Unless you are absolutely sure that nothingunusual can happen, you should use the identical() function instead.

� identical() only returns a single logical value, TRUE or FALSE, never NA

> name <- "Nick"

> if(name=="Nick") TRUE else FALSE

[1] TRUE

> # But what if name is never set to "Nick"?

> name <- NA

> if(name=="Nick") TRUE else FALSE

Error in if (name == "Nick") TRUE else FALSE :

missing value where TRUE/FALSE needed

> if(identical(name, "Nick")) TRUE else FALSE

[1] FALSE

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Isn’t that equal?

� With all.equal() objects are treated as equal if the only difference isprobably the result of inexact floating-point calculations. Returns TRUE ifthe mean relative difference is less then the specified tolerance.

� all.equal() either returns TRUE or a character string that describes thedifference. Therefore, do not use all.equal() directly in if expressions,instead use with isTRUE() or identical().

> (x <- sqrt(2))

[1] 1.414214

> x^2

[1] 2

> x^2==2

[1] FALSE

> all.equal(x^2, 2)

[1] TRUE

> all.equal(x^2, 1)

[1] "Mean relative difference: 0.5"

> isTRUE(all.equal(x^2, 1))

[1] FALSE

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Character

� Character strings are defined by quotation marks, single ’ ’ or double " "

cat() Concatenate objects and print to console (\n for newline)paste() Concatenate objects and return a stringprint() Print an objectsubstr() Extract or replace substrings in a character vectorstrtrim() Trim character vectors to specified display widthsstrsplit() Split elements of a character vector according to a substring

grep() Search for matches to a pattern within a character vector,returns a vector of the indices that matched

grepl() Like grep(), but returns a logical vectoragrep() Similar to grep(), but searches for approximate matchesregexpr() Similar to grep(), but returns the position of the first

instance of a pattern within a stringgsub() Replace all occurrences of a pattern with a character vectorsub() Like gsub(), but only replaces the first occurrence

tolower(), toupper() Convert to all lower/upper casenoquote() Print a character vector without quotationsnchar() Number of charactersletters, LETTERS Built-in vector of lower and upper case letters

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Example - Character Functions

animals <- c("bird", "horse", "fish")

home <- c("tree", "barn", "lake")

length(animals) # Number of strings

nchar(animals) # Number of characters in each string

cat("Animals:", animals) # Need \n to move cursor to a newline

cat(animals, home, "\n") # Joins one vector after the other

paste(animals, collapse=" ") # Create one long string of animals

a.h=paste(animals, home, sep=".") # Pairwise joining of animals and home

# Split strings at ".", fixed=TRUE since "." is used for pattern matching

unlist(strsplit(a.h, ".", fixed=TRUE))

substr(animals, 2, 4) # Get characters 2-4 of each animal

strtrim(animals, 3) # Print the first three characters

toupper(animals) # Print animals in all upper case

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Example - Pattern Matching� A regular expression is a pattern that describes a set of strings.

� ˆ Start of character string� $ End of character string� . Any character� .{n} Any n characters� [· − ·] Range of letters, i.e. [a-c] is a, b, c

� See ?regexp for more options

# colors() is a character vector of all the built-in color names

colors()[grep("red", colors())] # All colors that contain "red"

colors()[grep("^red", colors())] # Colors that start with "red"

colors()[grep("red$", colors())] # Colors that end with "red"

colors()[grep("red.", colors())] # Colors with one character after "red"

colors()[grep("^[r-t]", colors())] # Colors that begin with r, s, or t

places <- c("home", "zoo", "school", "work", "park")

gsub("o", "O", places) # Replace all "o" with "O"

sub("o", "O", places) # Replace the first "o" with "O"

# Capitalize the first letter, uses Perl-like regular expressions

gsub("(\\w)(\\w*)", "\\U\\1\\L\\2", places, perl=TRUE)33 of 45


Factor

� A factor is a categorical variable with a defined number of ordered orunordered levels. Use the function factor to create a factor variable.

> factor(rep(1:2, 4), labels=c("trt.1", "trt.2"))

[1] trt.1 trt.2 trt.1 trt.2 trt.1 trt.2 trt.1 trt.2

Levels: trt.1 trt.2

> factor(rep(1:3, 4), labels=c("low", "med", "high"), ordered=TRUE)

[1] low med high low med high low med high low med high

Levels: low < med < high

levels(x) Retrieve or set the levels of x

nlevels(x) Return the number of levels of x

relevel(x, ref) Levels of x are reordered so that the level specified by ref is firstreorder() Reorders levels based on the values of a second variablegl() Generate factors by specifying the pattern of their levelscut(x, breaks) Divides the range of x into intervals (factors) determined by breaks

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Example - Factor Functions

# Generate factor levels for 3 treatments and 2 cases per treatment

f <- gl(3, 2, labels=paste("trt",1:3, sep="."))

levels(f)

nlevels(f)

relevel(f, "trt.2")

x <- runif(10)

cut(x, 3) # Cut x into three intervals

cut(x, c(0,.25,.5,.75,1)) # Cut x at the given cut points

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Dates and Times

� R has objects that are dates only and objects that are dates and times. Wewill just focus on dates. Look at ?DateTimeClasses for information abouthow to handles dates and times.

� An R date object has the format: Year -Month-Day� Operations with dates,

� Days can be added or subtracted to a date� Dates can be subtracted� Dates can be compared using logical operators

Sys.Date() Current dateas.Date() Convert a character string to a date objectformat.Date() Change the format of a date objectseq.Date() Generate sequence of datescut.Date() Cut dates into intervalsweekdays, months, quarters Extract parts of a date objectjulian Number of days since a given origin

.Date suffix is optional for calling format.Date(), seq.Date() and cut.Date(),

but is necessary for viewing the appropriate documentation

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Convert Strings to Date Objects� Converting a string to a date object requires specifying a format string that

defines the date format� Any character in the format string other then the % symbol is interpreted

literally.� Common conversion specifications (see ?strptime for a complete list),

%a Abbreviated weekday name%A Full weekday name%d Day of the month%B Full month name%b Abbreviated month name%m Numeric month (01-12)%y Year without century (be very careful)%Y Year with century

> dates.1 <- c("5jan2008", "19aug2008", "2feb2009", "29sep2009")

> as.Date(dates.1, format="%d%b%Y")

[1] "2008-01-05" "2008-08-19" "2009-02-02" "2009-09-29"

> dates.2 <- c("5-1-2008", "19-8-2008", "2-2-2009", "29-9-2009")

> as.Date(dates.2, format="%d-%m-%Y")

[1] "2008-01-05" "2008-08-19" "2009-02-02" "2009-09-29"37 of 45


Sequence of Dates

� To create a sequence of dates,

seq.Date(from, to, by, length.out = NULL)

from, to Start and ending date objectsby A character string, containing one of ”day”, ”week”,

”month” or ”year”. Can optionally be preceded by a (positiveor negative) integer and a space, or followed by a ”s”.

length.out Integer, desired length of the sequence

> seq.Date(as.Date("2011/1/1"), as.Date("2011/1/31"), by="week")

[1] "2011-01-01" "2011-01-08" "2011-01-15" "2011-01-22" "2011-01-29"

> seq.Date(as.Date("2011/1/1"), as.Date("2011/1/31"), by="3 days")

[1] "2011-01-01" "2011-01-04" "2011-01-07" "2011-01-10" "2011-01-13"

[6] "2011-01-16" "2011-01-19" "2011-01-22" "2011-01-25" "2011-01-28"

[11] "2011-01-31"

> seq.Date(as.Date("2011/1/1"), by="week", length.out=10)

[1] "2011-01-01" "2011-01-08" "2011-01-15" "2011-01-22" "2011-01-29"

[6] "2011-02-05" "2011-02-12" "2011-02-19" "2011-02-26" "2011-03-05"

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Cutting Dates

� To divide a sequence of dates in to levels,cut.Date(x, breaks, start.on.monday = TRUE)

> jan <- seq.Date(as.Date("2011/1/1"), as.Date("2011/1/31"), by="days")

> cut(jan, breaks="weeks")

[1] 2010-12-27 2010-12-27 2011-01-03 2011-01-03 2011-01-03 2011-01-03

[7] 2011-01-03 2011-01-03 2011-01-03 2011-01-10 2011-01-10 2011-01-10

[13] 2011-01-10 2011-01-10 2011-01-10 2011-01-10 2011-01-17 2011-01-17

[19] 2011-01-17 2011-01-17 2011-01-17 2011-01-17 2011-01-17 2011-01-24

[25] 2011-01-24 2011-01-24 2011-01-24 2011-01-24 2011-01-24 2011-01-24

[31] 2011-01-31

6 Levels: 2010-12-27 2011-01-03 2011-01-10 2011-01-17 ... 2011-01-31

January 2011Sun Mon Tue Wed Thr Fri Sat26 27 28 29 30 31 1

2 3 4 5 6 7 8

9 10 11 12 13 14 15

16 17 18 19 20 21 22

23 24 25 26 27 28 29

30 31 1 2 3 4 5 39 of 45


Operations with Dates

� Operations with dates,� Days can be added or subtracted to a date� Dates can be subtracted� Dates can be compared using logical operators

> jan1 <- as.Date("2011/1/1")

> (jan8 <- jan1 + 7) # Add 7 days to 2011/1/1

[1] "2011-01-08"

> jan1 - 14 # Subtract 2 weeks from 2011/1/8

[1] "2010-12-18"

> jan8 - jan1 # Number of days between 2011/1/1 and 2011/1/8

Time difference of 7 days

> jan8 > jan1 # Compare dates

[1] TRUE

> # Use format to extract parts of a date object or change the appearance

> format.Date(jan8, "%Y")

[1] "2011"

> format.Date(jan8, "%b-%d")

[1] "Jan-01"40 of 45


Missing Data

� R denotes data that is not available by NA� How a function handles missing data depends on the function. For example

mean only ignores NAs if the argument na.rm=TRUE, whereas which alwaysignores missing data.> x <- c(4, 7, 2, 0, 1, NA)

> mean(x)

[1] NA

> mean(x, na.rm=TRUE)

[1] 2.8

> which(x>4)

[1] 2

� See the documentation for how a particular function handles missing data.� Quantities that are not a number, such as 0/0, are denoted by NaN. In R

NaN implies NA (NaN refers to unavailable numeric data and NA refers to anytype of unavailable data)

� Undefined or null objects are denoted in R by NULL. This is useful when wedo not want to add row labels to a matrix. For example,x <- matrix(1:4, ncol=2, dimnames=list(NULL, c("c.1", "c.2")))

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Detecting Missing Data� To test for missing data avoid using identical() and never use ==. Using

identical() relies on unreliable internal computations and == will alwaysevaluate to NA or NaN.

� Functions used for detecting missing data,is.na(x) Tests for NA or NaN data in x

is.nan(x) Tests for NaN data in x

is.null(x) Tests if x is NULL

> x <- c(4, 7, 2, 0, 1, NA)

> x==NA

[1] NA NA NA NA NA NA

> is.na(x)

[1] FALSE FALSE FALSE FALSE FALSE TRUE

> any(is.na(x))

[1] TRUE

> (y <- x/0)

[1] Inf Inf Inf NaN Inf NA

> is.nan(y)

[1] FALSE FALSE FALSE TRUE FALSE FALSE

> is.na(y)

[1] FALSE FALSE FALSE TRUE FALSE TRUE 42 of 45


Testing and Coercing Objects

� All objects in R have a type. We can test the type of an object using ais.type() function.

� We can also attempt to coerce objects of one type to another using aas.type() function.

� Automatic conversions,� Logical values are converted to numbers by setting FALSE as 0 and TRUE as 1� Logical, numeric, factor and date types are converted to characters by

converting each element/level individually

� Some general rules for coercion,� Numeric values are coerced to logical by treating all non-zero values as TRUE

� Numeric characters can be coerced to numbers, but non-numeric characterscannot

� Factor levels can be coerced to numeric and numbers can be coerced tofactors with a level for each unique number

� Vectors, matrices and arrays are coerced to lists by making each element avector of length 1

� Vectors, matrices, arrays can also be coerced from one form to another

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Testing and Coercing Functions

Type Testing CoercingArray is.array() as.array()

Character is.character() as.character()

Dataframe is.data.frame() as.data.frame()

Factor is.factor() as.factor()

List is.list() as.list()

Logical is.logical() as.logical()

Matrix is.matrix() as.matrix()

Numeric is.numeric() as.numeric()

Vector is.vector() as.vector()

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Example - Testing and Coercing Objects> x <- 1:10

> x>5

[1] FALSE FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE

> sum(x>5) # Automatic conversion to numeric vector

[1] 5

> is.vector(x)

[1] TRUE

> is.numeric(x)

[1] TRUE

> as.list(x)

[[1]]

[1] 1

[[2]]

[1] 2

. . .

[[10]]

[1] 10

> as.numeric("123")

[1] 123

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data structures and data types - lecture 2pitt.edu/~njc23/lecture2.pdf · data structures and data...

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